Write three fractions equivalent to 48/72
The Correct Answer and Explanation is:
Three Fractions Equivalent to 48/72:
- 2/3
- 4/6
- 16/24
Explanation
To find fractions equivalent to 48/72, we need to understand what it means for two fractions to be equivalent. Two fractions are equivalent if they represent the same value or proportion, even though they may look different. For example, 1/2 is the same as 2/4, because if you divide something into 2 parts and take 1, it is the same as dividing it into 4 parts and taking 2.
Now let’s take the fraction 48/72. To find an equivalent fraction, you can either simplify or scale it:
1. Simplifying 48/72
We start by finding the Greatest Common Divisor (GCD) of 48 and 72.
- Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
- Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
- The GCD is 24
Now divide the numerator and denominator by 24: 48÷2472÷24=23\frac{48 \div 24}{72 \div 24} = \frac{2}{3}
So, 2/3 is the simplest form of 48/72.
2. Scaling Up 2/3 to Get Another Equivalent Fraction
Multiply both the numerator and denominator of 2/3 by 2: 2×23×2=46\frac{2 \times 2}{3 \times 2} = \frac{4}{6}
So, 4/6 is equivalent to 48/72 as well.
3. Scaling 2/3 by 8
2×83×8=1624\frac{2 \times 8}{3 \times 8} = \frac{16}{24}
So, 16/24 is also equivalent to 48/72.
Conclusion:
Equivalent fractions are just different ways of expressing the same part of a whole. You can find them by simplifying or multiplying the numerator and denominator by the same number. 2/3, 4/6, and 16/24 are all equivalent to 48/72.
